Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.util.*;

public class RookBishopKing {

    public static void main (String[] args)
    {       
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        List<Integer> tri= new ArrayList<Integer>();
        for (int i=1;;i++){
            long k = (long) i*(i+1)/2;
            if (k>n) break;
            else tri.add((int)k);
        }

        int size = tri.size();
          //      for (int i=0;i<size;++i) System.out.print(tri.get(i) + " " );
        boolean found = false;
        int r1=-1, r2=-1;
        for (int i=0; i < size && found == false; ++i){
            int rem = n-tri.get(i);
            int l=0, r = size-1;
            while (l<=r){
                int mid = (l+r)/2;
                if (tri.get(mid)==rem){
                    r1 = i;
                    r2 = mid;
                    found = true;
                    break;
                }else if (tri.get(mid) <rem) l = mid + 1;
                else r = mid - 1;
            }
        }
        if (found == false) System.out.println("NO");
        else System.out.println("YES");
        sc.close();
    }
}